# Size of variable arrays:
sizeAlgebraic = 1
sizeStates = 1
sizeConstants = 6
from math import *
from numpy import *
def createLegends():
legend_states = [""] * sizeStates
legend_rates = [""] * sizeStates
legend_algebraic = [""] * sizeAlgebraic
legend_voi = ""
legend_constants = [""] * sizeConstants
legend_voi = "t in component y_channel (millisecond)"
legend_states[0] = "y in component y_channel (dimensionless)"
legend_constants[0] = "V in component y_channel (millivolt)"
legend_constants[1] = "E_y in component y_channel (millivolt)"
legend_algebraic[0] = "i_y in component y_channel (microA_per_cm2)"
legend_constants[2] = "g_y in component y_channel (milliS_per_cm2)"
legend_constants[3] = "gamma in component y_channel (dimensionless)"
legend_constants[4] = "alpha_y in component y_channel (per_millisecond)"
legend_constants[5] = "beta_y in component y_channel (per_millisecond)"
legend_rates[0] = "d/dt y in component y_channel (dimensionless)"
return (legend_states, legend_algebraic, legend_voi, legend_constants)
def initConsts():
constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
states[0] = 0
constants[0] = 0
constants[1] = -85
constants[2] = 36
constants[3] = 4
constants[4] = 1
constants[5] = 2
return (states, constants)
def computeRates(voi, states, constants):
rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
rates[0] = constants[4]*(1.00000-states[0])-constants[5]*states[0]
return(rates)
def computeAlgebraic(constants, states, voi):
algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
states = array(states)
voi = array(voi)
algebraic[0] = constants[2]*(power(states[0], constants[3]))*(constants[0]-constants[1])
return algebraic
def solve_model():
"""Solve model with ODE solver"""
from scipy.integrate import ode
# Initialise constants and state variables
(init_states, constants) = initConsts()
# Set timespan to solve over
voi = linspace(0, 10, 500)
# Construct ODE object to solve
r = ode(computeRates)
r.set_integrator('vode', method='bdf', atol=1e-06, rtol=1e-06, max_step=1)
r.set_initial_value(init_states, voi[0])
r.set_f_params(constants)
# Solve model
states = array([[0.0] * len(voi)] * sizeStates)
states[:,0] = init_states
for (i,t) in enumerate(voi[1:]):
if r.successful():
r.integrate(t)
states[:,i+1] = r.y
else:
break
# Compute algebraic variables
algebraic = computeAlgebraic(constants, states, voi)
return (voi, states, algebraic)
def plot_model(voi, states, algebraic):
"""Plot variables against variable of integration"""
import pylab
(legend_states, legend_algebraic, legend_voi, legend_constants) = createLegends()
pylab.figure(1)
pylab.plot(voi,vstack((states,algebraic)).T)
pylab.xlabel(legend_voi)
pylab.legend(legend_states + legend_algebraic, loc='best')
pylab.show()
if __name__ == "__main__":
(voi, states, algebraic) = solve_model()
plot_model(voi, states, algebraic)